Abstract
At low energies, interactions of massless particles in type II strings compactified on a torus Td are described by an effective Wilsonian action \( \mathcal{S} \)(Λ), consisting of the usual supergravity Lagrangian supplemented by an infinite series of higher-derivative vertices, including the much studied Δ4p + 6qℛ4 gravitational interactions. Using recent results on the asymptotics of the integrands governing four-graviton scattering at genus one and two, I determine the Λ-dependence of the coefficient of the above interaction, and show that the logarithmic terms appearing in the limit Λ → 0 are related to UV divergences in supergravity amplitudes, augmented by stringy interactions. This provides a strong consistency check on the expansion of the integrand near the boundaries of moduli space, in particular it elucidates the appearance of odd zeta values in these expansions. I briefly discuss how these logarithms are reflected in non-analytic terms in the low energy expansion of the string scattering amplitude.
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Pioline, B. String theory integrands and supergravity divergences. J. High Energ. Phys. 2019, 148 (2019). https://doi.org/10.1007/JHEP02(2019)148
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DOI: https://doi.org/10.1007/JHEP02(2019)148